Fitting Charts

NOTE 4: I was always puzzled about the 4cpm or so slope on most fitting
charts. Why is the 9 iron stiffer, cpm wise, than the 2 iron? Did somebody
just dream this up? I know some clubmakers that swear by flatlining
a set of clubs. When I looked at the equation of a cantilever beam (Tech
Note 1) with its variables in the denominator and a cube term and square
roots etc., it sure didn't appear to be a straight-line function by
any stretch of the imagination. I decided to do a little paper exercise
(spread sheets are the second best thing since sliced bread) and plotted
the equation knowing that each club in the set gets shorter while the
head gets heavier and the shaft gets a bit lighter. The material didn't
change and the cross sectional shape remains the same throughout the
set. I assumed the term EI therefore was constant throughout the set.
I computed the term EI from a given frequency of the first club in the
set (292cpm for a 40" 225 gram 1 iron with a 125 gram shaft). The frequency
of each club was then computed using the equation in Tech Note 1. The
following assumptions were made: Each successive club is ½ inch shorter,
each head is 7 grams heavier and each shaft is 1.6 grams lighter. The
length used in the equation is the club length minus the 5 inch clamping
length. I then plotted this derived frequency of each club to see what
the curve looked like. I was happy to get a fairly straight like with
a slope gradually increasing from 2.5 cpm/club to 4.4 cpm/club. I guess
the fitting charts do have some mathematical heritage. This also indicates,
that at least theoretically, the fitting charts should have a slope
of about 3 cpm per club. Contact me if you want more details.

Club
1
2
3
4
5
6
7
8
9
P

CPM
292.0
294.5
297.3
300.3
303.5
306.9
310.5
314.4
318.6
323.0

Slope

2.5
2.8
3.0
3.2
3.4
3.6
3.9
4.2
4.4

(First cpm selected, approx. R flex)

Using this approach I then worked backwards into the woods starting
with a 41" 5 wood and continuing on to a 44" driver. Unfortunately there's
significant discontinuity between the 5 wood and the 1 iron, about 10
cpm. I'm still scratching my head trying to figure out what this means
in terms of club fitting. I'll put the plot in a future Tech Note.

...some time later...

Oops! Well I thought about it some more and realized that I must be
senile in my old age. In the above interesting yet seriously flawed
exercise I assumed the term I in the equation was a constant. The term,
I, is dependent on the cross-sectional shape of the shaft. Since the
shaft is tapered or stepped its value must change as you butt or tip
trim the shaft. If I was constant throughout it would be impossible
to flatline a set of clubs.

Just to check I took an AP50 shaft and attached a test weight to the
tip whose weight I could change very accurately. Using the same weight
club heads as I did in my flawed exercise I butt trimmed the "set" and
got essentially a flat line frequency result. I then repeated the process,
this time tip trimming in ½" steps. I got roughly a 4cpm per club slope.